Based on the classic paper by Holling in 1959, predator-prey interaction can be modeled by the following functions (i.e. so called Type I or Type II functional response). Both functional responses contains a parameter that describes the proportion of prey that is available for the predator.
\[f(R) = {\alpha}TR \], where \({\alpha}\) is the encounter probability, \(T\) is the searching time, and \(R\) is the prey density. Encounter probability (\({\alpha}\)) is the proportion of prey that is available for the predator.
\[f(R) = \frac{{\alpha}TR}{1+{\alpha}hR}\], where \({\alpha}\) is again the encounter probability, \(T\) is the searching time, and \(h\) is the handling time.
In my lab experiment, I directly modified the \({\alpha}\) parameter because I used the screen mesh to modify the proportion of IG prey that is available to the IG predator. This lab experiment would thus be valid to verify my model predictions.
First visualize the population dynamics of the two protozoa species.
Blepharisma
Colpidium
Now I take the hour 368, 414, 468, 486, and 535 to calculate the mean and standard error of two protozoa density in the six treatments (0%, 20%, 40%, 60%, 80%, and 100% encounter probability).
From the model I derive three major predictions.
Here I extract the IG prey density at the equilibrium from the model. According to the model that used type I functinoal response to model intra-guild predation, I would expect the IG prey density to monotonically decrease with encounter probability.
IG prey density at equilibrium in the model
Here I calculate the mean IG prey (Colpidium) density across the six treatments (0%, 20%, 40%, 60%, 80% and 100% encounter probability)
The two plots does not match. This mismatch suggests to me that the type I functional response in the model is not proper to describe the population dynamics of IG prey and IG predator.
Here I extract the IG predator density at the equilibrium from the model. According to the model that used type I functinoal response to model intra-guild predation, I would expect the IG predator density to monotonically increase with encounter probability.